Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations

2023/04/26 by Pablo D. Carrasco, Carrasco, Pablo D., Federico Rodríguez-Hertz +1
Mathematics · Physics and Astronomy · #37D30 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2304.13384

openalex publication_date 2023/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to Hölder potentials satisfy a strong rigidity property: they are determined only by their disintegrations on (strong) stable or unstable leaves. As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is Hölder, without any restriction on the dimension of the invariant distributions. This gives another proof of a result of Babillott-Ledrappier.

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